Scoop the avocado flesh into a blender. Add the sour cream and the juice of 1/2 lime and pulse until smooth. Season with salt.
Squeeze the remaining 1/2 lime over the radishes in a small bowl and sprinkle with 1/4 teaspoon salt. Toss the chicken with 3/4 cup salsa in a medium bowl.
Heat 3/4 inch of vegetable oil in a Dutch oven or large skillet over medium-high heat until a deep-fry thermometer registers 375 degrees F.
Meanwhile, wrap the tortillas in paper towels and microwave until soft, about 45 seconds. Spoon the chicken mixture down the middle of the tortillas. Fold in the ends and roll up like a burrito; secure with toothpicks.
Working in batches, fry the flautas in the oil, turning as needed, until golden brown, 2 to 3 minutes. Remove with tongs; drain on paper towels and remove the toothpicks. Serve with the avocado cream, radishes, cilantro, lime wedges and the remaining 3/4 cup salsa.
Courtesy of Food Network Magazine, Photograph by Antonis Achilleos